Went to the tyre place this morning and had my wheels swapped front to back. They balanced them again. It turns out that both the original continental tyres are a bit out of shape. The tyres are cracked in between the tread too. Now the continentals are back on the rear the shaky steering wheel problem has stopped. So it turned out to be an expensive job as I've just ordered another two Goodyear tyres at £112 each. At least it'll be sorted next week.
